A191834 Numbers n not divisible by 2 or 3 such that k^k == k+1 (mod n) has no nonzero solutions.

205, 301, 455, 1015, 1025, 1085, 1435, 1505, 2107, 2255, 2275, 2485, 2665, 3185, 3311, 3485, 3895, 3913, 4715, 4823, 5005, 5075, 5117, 5125, 5425, 5467, 5719, 5915, 5945, 6355, 6923, 7105, 7175, 7525, 7585, 7595, 7735, 8405, 8645, 8729, 8815, 9331, 9635, 10045, 10465, 10535, 10865, 11137, 11165, 11275, 11375, 11935, 12095

Offset: 1

Author

Franklin T. Adams-Watters, Jun 17 2011

Keywords

• nonn

Comments

Values of A007310(n) for n such that A191833(n) = 0.

This sequence contains no primes. If p is a prime, and r is a primitive root of p, the numbers (r+j*p)^(r+j*p) for j = 1..p-1 include all residues of units mod p, and for p > 3, r+1 must be a unit.

The complete list of n such that k^k == k+1 (mod n) has no nonzero solutions is the union of A047229 and this sequence.

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A191833, A191835 (primitive elements).

Programs

Mathematica

A191833[n_] := (For[m = 2*n + 2*Floor[n/2] - 1; k = 1, k <= m^2, k++, If[PowerMod[k, k, m] == Mod[k+1, m], Return[{k, m}]]]; {0, m}); Reap[For[j = 1; n = 1, n <= 5000, n++, {z, m} = A191833[n]; If[z == 0, Print["a(", j++, ") = ", m]; Sow[m]]]][[2, 1]] (* Jean-François Alcover, Sep 13 2013 *)

Extensions

Terms a(30) onward from Max Alekseyev, Sep 10 2013